Mathematics 1. An equation representing a function that extends from quadrant 2 to quadrant 4 is a. y = x 3 b. y = 2x 5 c. y = 2x 6 d. y = 5x 4 2. The degree of the polynomial function is a. 3 b. 4 c. 5 d. 6 3. The function y = 2x 2 (x 1)(x 2)2 changes sign at a. x = 1 b. x = 0 c. x = 1 d. it doesnt change sign 4. Which of the following is a polynomial function? a. y = sin x b. y = cos x c. y = 3x d. y = x 3 5. Which of the following is an odd function? a. y = 2x 3 + x 2 b. y = 2x 4 + 11 c. y = 2x 4 x d. y = x 3 + x 5 6. The graph of the function y = x 4 is transformed to the graph of the function y = [2(x + 3)]4 + 1 by a. Vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up b. Horizontal stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up c. Vertical compression by a factor of , a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up d. Horizontal compression by a factor of , a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up 7. If 2x 3 9x 2 + 4x 7 is divided by x 3 to give a quotient of 2x 2 3x 5 and a remainder of 22 , then which of the following is true? a. 2x 3 9x 2 + 4x 7 = (x 3)(2x 2 3x 5) + 22 b. 2x 3 9x 2 + 4x 7 = (x 3)(2x 2 3x 5) 22 c. (x 3)(2x 2 3x 5) = 22 d. (x 3)(2x 2 3x 5) = 22 8. What is the maximum number of real distinct roots that a quartic equation can have? a. infinitely many b. 4 c. 2 d. none of the above 9. Which of the reciprocal functions has a vertical asymptote at ? a. b. c. d. 10. Which of the following is true? a. has two vertical asymptotes. b. is always negative. c. decreases over its entire domain. d. never increases. Page 2 of 6 Show all work from this point forward for full marks: 11. Solve the following: ??? & ??? a) b) 12. Determine the average rate of change of the function on the interval . ???? Part B Thinking and Investigation [TI 20 marks]. 1. Determine the approximate slope of the tangent to the curve at , to one decimal place. ???? 2. A stunt pilot is testing a new plane. The equation that models his height over time is , where x is his the time in seconds and f(x) is his height in metres. Determine when the pilot is below 450 metres.????? Page 3 of 6 3. The polynomial px 3 x 2 + qx 2 has no remainder when divided by (x 1) and a remainder of 18 when divided by (x + 2). What are the values of p and q? ?????? 4. Solve the following inequality using an algebraic method. ?? ??? Part C Communication [COMM 20 marks] ***Fully label your graphs for full marks!*** 1. Determine an equation for the graph of the polynomial function shown. ?? 2. Determine an equation in factored form for a polynomial function with zeros at 1 (order 2), 0 and and passes through the point (4, 5).??? 3. Write a quadratic inequality with the solution: x ? ( ) [<- this is the same as ] ??? 4. Consider the function. a) Determine the key features of the function: i) domain and range?? ii) intercepts?? iii) equations of any asymptotes ?? iv) intervals where the function is increasing and intervals where the function is decreasing?? b) Sketch a graph of the function. ? Part D Application [APP 12 marks] 1. Two resistors a and b are connected in parallel. The total resistance R in such a circuit is found by the formula R . If R ohms and b is one more ohm than a, find the number of ohms in a and b. (answers should be positive). ? 2. Factor fully (show your work). ? & ? a) b) 3. The area of a triangular-shaped wall is ) m . The base of the wall is (5x + 7) m long. How tall is the wall? ? PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET A GOOD DISCOUNT

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